Descriptive Properties of Spaces of Measures

Student: Novikov Lev

Educational Programme: Mathematics (Bachelor)

Final Grade: 8

Year of Graduation: 2018

The main goal of the paper is the search for some general properties of the measure space P(X), where the measures are defined on some arbitrary topological space X. We consider the results already available for locally compact separable spaces, made by Lange and Fell, and consider a more complicated case when the space of measures P(X) turns out to be not analytic. To do this, we will describe Borel sets for Polish spaces, in particular, with the help of Borel isomorphism we will translate the Borel structure (in fact, the set of Borel sets or the topology) of the Polish space of interest to the Borel structure generated by the usual topology in the Hilbert cube. The resulting structure will be defined on a metric separable space, which allows us to obtain some properties of measure spaces.

Full text (added June 4, 2018)

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses